Boundary driven instabilities of Couette flows

Abstract

In this article, we prove that the threshold of instability of the classical Couette flow in $H^s$ for large $s$ is $\nu^{1/2}$. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width $\nu^{1/2}$ which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.